In the book *Open Problems in Topology* by Jan Van Mill and George M. Reed, the following problem was presented:
108. *Is there a para- Lindelof Dowker space?*
Recall that a *para-Lindelof Dowker space* has a locally countable open refinement, satisfies Axiom T4, and is not countably paracompact.
Some results on this problem are in http://topology.auburn.edu/tp/reprints/v11/tp11203.pdf, where it is shown that the conditions are preserved under perfect mappings.
What is the status of this problem?
Any references are appreciated.

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